Let \(\otimes _{\min }\)  denote the spatial (minimal) tensor product.
Due to the fact that minimal tensor products preserve injections
(e.g., see [1]} or
[2]}),
for any unital \(C^*\) -algebras \(A_1\)  and \(A_2\)  the natural maps
\(A_1\ni a\longmapsto a\otimes 1\in A_1 \underset{\min }{\otimes } A_2\qquad \text{and}\qquad A_2\ni a\longmapsto 1\otimes a\in A_1 \underset{\min }{\otimes } A_2\) 
